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MHT CET · Physics · Waves and Sound

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length ' \(L\) '. The length of the open pipe will be

  1. A \(\frac{L}{2}\)
  2. B \(\mathrm{L}\)
  3. C \(\mathrm{2L}\)
  4. D \(\mathrm{4L}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\mathrm{2L}\)

Step-by-step Solution

Detailed explanation

The length of closed pipe is denoted using \(\mathrm{L}\). Let \(l\) be the length of open pipe and \(\mathrm{v}\) be the velocity.

Frequency of second overtone of an open organ pipe is \(\mathrm{n}_{\mathrm{o}}=\frac{3 \mathrm{v}}{2 l}\)

Frequency of first overtone of a closed pipe is \(\mathrm{n}_{\mathrm{c}}=\frac{3 \mathrm{v}}{4 \mathrm{~L}}\)

Given: \(\mathrm{n}_0=\mathrm{n}_{\mathrm{c}}\)
\(\frac{3 \mathrm{v}}{2 l}=\frac{3 \mathrm{v}}{4 \mathrm{~L}}\)
\(\mathrm{L}=\frac{l}{2}\)
\(\therefore \quad l=2 \mathrm{~L}\)